Question

If the expression X² - 11x + a and x²- 14x + 2a must have a common factor and a not =0. then the
common factor is

​

Answer 1

Answer:

a=24, then polynomials will become

x^2-11x+24 and x^2-14x+48

which can be written as 

(x-8)*(x-3) and (x-8)*(x-6)

(x-8) is common factor.

first put a=24

the 2 equations solved and get the common factor 8.

it will not be factorised easily and eventhough factorising therw will be no common term found out.

Hence definetly 24 will be the answera=24, then polynomials will become

Answer 2

» x² - 11x + a and x² - 14x + 2a. Both have common factor.

Means.. both the expressions are equal to each other.

i.e.

=> x² - 11x + a = x² - 14x + 2a

=> x² - x² - 11x + 14x + a - 2a = 0

=> 3x - a = 0

=> 3x = a

=> x = a/3 __________ (eq 1)

_______________________________

Now..

First put value of x in x² - 11x + a and then in x² - 14x + 2a.

=> (a/3)² - 11(a/3) + a = 0

=> a²/9 - 11a/3 + a = 0

=> a²/9 = 11a/3 - a

=> a²/9 = (11a - 3a)/3

=> a²/9 = 8a/3

=> a² = (8a × 9)/3

=> a² = 24a

=> a = 24

We get the same result by putting value of x in x² - 14x + 2a.

_____________________________

24 is the common factor of both the expressions.

_________ [ ANSWER ]

_____________________________